Prove that: 4 x=1-8 ^2 x ^2 x - Vidyadip

Question

Prove that: $\cos 4 x=1-8 \sin ^2 x \cos ^2 x$

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Answer

We have L.H.S. $=\cos 4 \mathrm{x}=1-2 \sin ^2 2 \mathrm{x}\left[\because \cos 2 \theta=1-2 \sin ^2 \theta\right]$
$=1-2(2 \sin x \cos x)^2[\because \sin 2 \theta=2 \sin \theta \cos \theta]$
$=1-2\left(4 \sin ^2 x \cos ^2 x\right)$
$=1-8 \sin ^2 x \cos ^2 x=\text { R.H.S. }$

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